Set of Natural Numbers is Smallest Ordinal Greater than All Natural Numbers
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Theorem
The set of natural numbers $\N$ is the smallest ordinal which is greater than all natural numbers.
Proof
From Set of Natural Numbers is Ordinal, $\N$ is an ordinal.
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Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 3$ Some ordinals